As lithography techniques continue to advance to meet the ever-increasing need for higher power computing chips1, more advanced thermal management is needed to prevent thermal degradation and proper system operation2. This need is present across the range of computational power from desktop PCs to data centers3. Triply periodic minimal surfaces (TPMS) are mathematically defined structures with a high degree of symmetry and surface area to volume ratios, and exhibit controllable periodicity with zero-mean curvature. TPMS lattices have been studied extensively in engineering applications including structural lightweighting4 and heat transfer5,6. High complexity makes TPMS lattices difficult to manufacture and additive manufacturing (AM) is particularly suited to manufacturing this class of geometries. Choosing the best TPMS lattice parameters is difficult due to the large design space and conflicting parameters. Previous studies have focused on a small subset of the TPMS design space to determine heat transfer performance of various TPMS designs. In this study, we implemented a computational optimization approach using OpenFOAM to optimize six different TPMS types (Diamond, Schwarz, Neovius, Gyroid, SplitP, and Lidinoid) in forced convection in three scenarios. We explored both cylindrical and rectangular functionally graded heat sinks. Three cases (I-III) were explored changing the optimization constraints of pressure drop and flowrate. The optimized designs were printed in AlSi10Mg using an L-PBF printer and tested experimentally. The Lidinoid Case I design was found to have the lowest thermal resistance of 0.78 W/K, 16 % lower than the standard plate fin design. When normalized for mass, the Schwarz Case II design had a 71 % lower normalized thermal resistance than the baseline plate fin design. Custom heat sink performance could be achieved by varying the fitness function constraints during optimization. Using this technique, heat sink designers can explore a greater design space to improve thermal management capabilities.